integral of x^2e^{x/6}

Lösung

\int x^{2} e^{\frac{x}{6}} d x

6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}}) + C

Schritte zur Lösung

\int x^{2} e^{\frac{x}{6}} d x

Wende die partielle Integration an

= 6 e^{\frac{x}{6}} x^{2} - \int 12 e^{\frac{x}{6}} x d x

\int 12 e^{\frac{x}{6}} x d x = 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})

= 6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})

Füge eine Konstante zur Lösung hinzu

= 6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}}) + C

\frac{\partial}{\partial x} (- x yz + 54)

d er i v a t i v e 3 e^{x^{2}}

t an g e n t f (x) = \frac{1}{3} x^{3} - 14 x^{2} + 6 x + 1

\frac{d}{d x} (- x + \frac{8}{x} + 1)

y^{^{''}} + 10 y^{^{'}} + 24 y = 0